These, when a thousand rolling years are o’er,
Called by the God, to Lethe’s waves repair;
There, reft of memory, to yearn once more
For mortal bodies and the upper air.

[Has omnis, ubi mille rotam volvere per annos,
Lethaeum ad fluvium deus evocat agmine magno,
Scilicet immemores supera et convexa revisant
Bursus et incipiant in corpora velle reverti.]

Virgil (70-19 BC) Roman poet [b. Publius Vergilius Maro; also Vergil]

The Aeneid [Ænē̆is], Book 6, l. 748ff (6.748-751) [Anchises] (29-19 BC) [tr. Taylor (1907), st. 99, l. 883ff]
    (Source)

On the reincarnation of most souls, other than those punished in Tartarus or rewarded in Elysium.

(Source (Latin)). Alternate translations:

When thousand yeares have fil'd their period,
All these God calls in troups to Lethe's flood,
To th end that they forgetfull of what's past,
May reascend, and bodies take at last.
[tr. Ogilby (1649)]

But, when a thousand rolling years are past,
(So long their punishments and penance last,)
Whole droves of minds are, by the driving god,
Compell'd to drink the deep Lethaean flood,
In large forgetful draughts to steep the cares
Of their past labors, and their irksome years,
That, unrememb'ring of its former pain,
The soul may suffer mortal flesh again.
[tr. Dryden (1697)]

All these, after they have rolled away a thousand years, are summoned forth by the god in a great body to the river Lethe; to the intent that, losing memory, they may revisit the vaulted realms above, and again become willing to return into bodies.
[tr. Davidson/Buckley (1854)]

All these, when centuries ten times told
The wheel of destiny have rolled,
The voice divine from far and wide
Calls up to Lethe's river-side,
That earthward they may pass once more
Remembering not the things before,
And with a blind propension yearn
To fleshly bodies to return.
[tr. Conington (1866)]

All these, when for a thousand years the wheel
Of fate has turned, the Deity calls forth
To Lethe's stream, a mighty multitude;
That they, forgetful of the past, may see
Once more the vaulted sky, and may begin
To wish return into corporeal frames.
[tr. Cranch (1872), l. 933ff]

All these before thee, when the wheel of a thousand years hath come fully round, a God summons in vast train to the river of Lethe, that so they may regain in forgetfulness the slopes of upper earth, and begin to desire to return again into the body.
[tr. Mackail (1885)]

All these who now have turned the wheel for many and many a year
God calleth unto Lethe's flood in mighty company,
That they, remembering nought indeed, the upper air may see
Once more, and long to turn aback to worldly life anew.
[tr. Morris (1900)]

At last, when the millennial aeon strikes,
God calls them forth to yon Lethaean stream,
In numerous host, that thence, oblivious all,
They may behold once more the vaulted sky,
And willingly to shapes of flesh return.
[tr. Williams (1910), l. 747ff]

A thousand years pass over
And the god calls the countless host to Lethe
Where memory is annulled, and souls are willing
Once more to enter into mortal bodies.
[tr. Humphries (1951)]

All these souls, when they have finished their thousand-year cycle,
God sends for, and they come in crowds to the river of Lethe,
So that, you see, with memory washed out, they may revisit
The earth above and begin to wish to be born again.
[tr. Day-Lewis (1952)]

But all the rest, when they have passed time's circle
for a millennium, arfe summoned by
the god to Lethe in a great assembly
that, free of memory, they may return
beneath the curve of the upper world, that they
may once again begin to wish for bodies.
[tr. Mandelbaum (1971), l. 988ff]

These other souls,
When they have turned Time's wheel a thousand years,
The god calls in a crowd to Lethe stream,
There there unmemoried they may see again
The heavens and wish re-entry into bodies.
[tr. Fitzgerald (1981), l. 1004ff]

All these others whom you see, when they have rolled the wheel for a thousand years, are called out by God to come in great columns to the river of Lethe, so that they may duly go back and see the vault of heaven again remembering nothing, and begin to be willing to return to bodies.
[tr. West (1990)]

All these others the god calls in a great crowd to the river Lethe,
after they have turned the wheel for a thousand years,
so that, truly forgetting, they can revisit the vault above,
and begin with a desire to return to the flesh.
[tr. Kline (2002)]

All these,
When they have rolled the wheel of time
Through a thousand years, will be called by God
In a great assembly to the river Lethe,
So that they return to the vaulted world
With no memory and may begin again
To desire rebirth in a human body.
[tr. Lombardo (2005)]

All the rest, once they have turned the wheel of time
for a thousand years: God calls them forth to the Lethe,
great armies of souls, their memories blank so that
they may revisit the overarching world once more
and begin to long to return to bodies yet again.
[tr. Fagles (2006), l. 865ff]

When the rest have cycled through a thousand years, the god calls them in clusters to the river Lethe. These forgetful spirits hope for resurrection into bodies. They start to want to see the sky.
[tr. Bartsch (2021)]